Each of the numbers 1 to 9 appears four times in the 6x6 grid. If a number appears twice in any row or column, it is mentioned in the relevant clue.

                 1  2  3  4  5  6
               +--+--+--+--+--+--+
            1  |  |  |  |  |  |  |
               +--+--+--+--+--+--+
            2  |  |  |  |  |  |  |
               +--+--+--+--+--+--+
            3  |  |  |  |  |  |  |
               +--+--+--+--+--+--+
            4  |  |  |  |  |  |  |
               +--+--+--+--+--+--+
            5  |  |  |  |  |  |  |
               +--+--+--+--+--+--+
            6  |  |  |  |  |  |  |
               +--+--+--+--+--+--+

ACROSS
1. Total 22.
2. The numbers in the first three cells are even; those in the last three are odd.
3. Two 5s, one of which is enclosed by two 1s. Total 27.
4. 7 and 9 are the only odd numbers.
5. No 2s, 3s or 9s.
6. Two 3s enclosing an 8. No 7s. Total 31.

DOWN
1. No 2s, 6s or 7s.
2. Two 7s separated by two squares. Four even numbers.
3. The sum of the lowest three cells is 14.
4. Total 21.
5. No 3s, 4s or 7s.
6. Two 9s separated by two squares. Total 39.